View source for Bully Mnemonic Extension

The '''Bully Mnemonic Extension''' is a technique for remembering the exact number of meters that light travels in one second, and the approximate range of gravitational accelerations that occur on the surface of the Earth due to Newton's law of universal gravitation. Using the ''Bully Mnemonic'' and ''Bully Mnemonic Extension'' in conjunction allows one to calculate a significant number of physical quantities, including the exact number of meters in a light year.


The following relationships are encoded in the Bully Mnemonic Extension:

<math display="block"> Speed \, of \, light \, in \, vacuum = {299,792,458 \, meters \, per \, second} </math>

<math display="block"> {High \, end \, of \, g_{Earth}} = {9.8624 \, meters \, per \, second^{2}} </math>

<math display="block"> {Low \, end \, of \, g_{Earth}} = {9.7644 \, meters \, per \, second^{2}} </math>


The following relationship can be derived using the ''Bully Mnemonic'' and ''Bully Mnemonic Extension'' in conjunction:

<math display="block"> 1 \, light \, year = {9,460,528,412,464,108 \, meters} </math>


= Bully Mnemonic Extension Steps =

== Initial Definitions ==

=== Step 1 ===

Complete steps 1 and 2 of the [[The Bully Mnemonic]] to form integers a) and b) as shown below:

<math display="block"> a) \, {\color{Red} 1} 0  {\color{Red} 33}  0 </math>
<math display="block"> b) \, {\color{Red} 3} 0  {\color{Red} 55}</math>

=== Step 2 ===

The Bully Mnemonic Extension will use two variants of integer a). The first variant will have 33 removed and replaced with 00.  The second variant will have 330 removed and replaced with 22:

<math display="block"> \begin{matrix} \scriptstyle\text{1} & {\color{Red} 2} &  \scriptstyle\text{3} & {\color{Red} 4} & \scriptstyle\text{5} \end{matrix} </math>

<math display="block"> av1) \, {\color{Red} 1} 0000 </math>
<math display="block"> av2) \, {\color{Red} 1} 0  {\color{Red} 22}</math>
<math display="block"> b) \, {\color{Red} 3} 0  {\color{Red} 55}</math>

== Speed of Light ==

=== Step 3 ===

Multiply integers av2) and b) from Step 2.

<math display="block"> {\color{Red} 1} 0 {\color{Red} 22} \times {\color{Red} 3} 0 {\color{Red} 55}  = 3122210

Using Long Multiplication: 
      3055
 ×    1022
 ————————————
      6110
     6110
    0000
   3055
 ————————————
   3122210

=== Step 4 ===

Drop the zero from the integer obtained in step 3, swap 2s and 3s, and swap 1s with 9s to obtain integer f) shown below:

    312221
 f) 293339

=== Step 5 ===

Multiply integer av2) from Step 2, and integer f) from step 4, to get the total number of meters that light travels in one second.

<math display="block"> {\color{Red} 1} 0 {\color{Red} 22} \times {\color{Red} 3} 0 {\color{Red} 55}  = 3122210

Using Long Multiplication: 
      3055
 ×    1022
 ————————————
      6110
     6110
    0000
   3055
 ————————————
   3122210

== Great Years ==

=== Step 6 ===

The Great Year is, by definition, a least common multiple of the sidereal year and the tropical year.  From steps 4 and 5 above, we have that the ratio of tropical years to sidereal years is:

<math display="block">{\frac{1 \, Tropical \, Year}{1 \, Sidereal \, Year}} \approx {\frac{(10330 - 0.40) \times 3055 \, sec}{10330 \times 3055 \, sec}} </math>

Divide top and bottom by amount d) and use the Distributive Property of Multiplication to obtain:

<math display="block"> {\frac{1 \, Tropical \, Year}{1 \, Sidereal \, Year}} \approx {\frac{(\frac{10330}{0.40} - \frac{0.40}{0.40}) \times 3055 \, sec}{(\frac{10330}{0.40}) \times 3055 \, sec}} </math>

From whence:

<math display="block"> {\frac{1 \, Tropical \, Year}{1 \, Sidereal \, Year}} \approx {\frac{(25825 - 1) \times 3055 \, sec}{(25825) \times 3055 \, sec}} </math>

Consequently:

<math display="block"> {\frac{25825 \, Tropical \, Year}{25824 \, Sidereal \, Year}} \approx {\frac{25825 \times (25824) \times 3055 \, sec}{25824 \times (25825) \times 3055 \, sec}} = 1 </math>

Finally:

<math display="block"> 1 \, Great \, Year \approx 25825 \, Tropical \, Years \approx 25824 \, Sidereal \, Years </math>

In terms of Long Multiplication; 0.40, 25825, and 10330 are related as follows: 
        0.40
 ×  25825
 ————————————
        2.00
       08.0
      320
     200
    080
 ————————————
    10330.00

== Galactic Years ==

=== Step 7 ===

Multiply integer c) by the square of integer a) to get a rough approximate galactic year (the number of tropical years required for the Solar System to orbit once around the galactic center).

<math display="block">{\color{Red} 2} \times {{\color{Red} 1} 0  {\color{Red} 33}  0}^{2} = 213417800 \approx \frac{ 1 \, Galactic \, Year}{ 1 \, Tropical \, Year} </math>

Using Long Multiplication: 
        10330
 ×      10330
 ——————————————
        00000
       30990
      30990
     00000
    10330
 ——————————————
    106708900

And finally:
 106708900 × 2 = 213417800